I've been playing around with getting both gain and offset on a single non-
inverting op amp and I'm not quite getting how to calculate the offset
input voltage needed to get 1.27 volts out. I'm hoping someone might know
what I'm missing.

What I attempted was to get 2.5x gain with a +1.25 volt offset - so a zero
volt input on the non-inverting input would give 1.25 volts out while a 1
volt input would give 3.75 volts out.

At first, I thought that since there was to be a 2.5x gain, I needed to add
-1.25/2.5= -0.5V to the inverting input. I used a voltage divider to create
the -0.5V. from the -5V supply.

Next I went to tackle the gain. I calculated the thevenin equivilent
resistance of the voltage divider then calculated the size of the feedback
resistor and put it all together on a breadboard.

I got the gain right - but with 0V in I get 0.750V out - which is only 1.5
times the offset voltage I supplied. Ok, so my assumption about the affect
of gain on the supplied offset voltage was wrong - I went looking on google
to see if I could find out how to calculate the voltage required: two days
ago!

To sum up: I'm using an LMC6482 CMOS amp with 10 teraohm input impedance.
Input signal is a 10k resistor to either ground or a voltage divider
putting out 1V. I can calculate the gain with Thevenin's but I cannot
figure out how to calculate the offset voltage required.

Anyone able to steer me in the right direction?

P.S. I have this working with two opamps (one chip). Its just bugging me
that I cannot figure out how to do it with a single stage.